A295922 - OEIS

%I #15 Dec 28 2022 10:37:26

%S 2,4,16,81,393,1777,7633,31745,129537,523009,2099969,8409089,33634305,

%T 134475777,537628673,2149580801,8595505153,34374090753,137475063809,

%U 549844942849,2199239786497,8796612067329,35185602068481,140740374036481,562956664307713

%N Number of (not necessarily maximal) cliques in the n-halved cube graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HalvedCubeGraph.html">Halved Cube Graph</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (13, -68, 184, -272, 208, -64).

%F a(n) = (24*(2 + 4^n) + 2^n*n*((n - 9)*n - 16))/48.

%F a(n) = 13*a(n-1) - 68*a(n-2) + 184*a(n-3) - 272*a(n-4) + 208*a(n-5) - 64*a(n-6).

%F G.f.: x (2 - 22*x + 100*x^2 - 223*x^3 + 236*x^4 - 96*x^5)/((-1 + 2*x)^4*(1 - 5*x + 4*x^2)).

%t Table[(24 (2 + 4^n) + 2^n n ((n - 9) n - 16))/48, {n, 20}]

%t LinearRecurrence[{13, -68, 184, -272, 208, -64}, {2, 4, 16, 81, 393, 1777}, 20]

%t CoefficientList[Series[(2 - 22 x + 100 x^2 - 223 x^3 + 236 x^4 - 96 x^5)/((-1 + 2 x)^4 (1 - 5 x + 4 x^2)), {x, 0, 20}], x]

%o (PARI) a(n)=(24*4^n+2^n*n*(n*(n-9)-16))/48+1 \\ _Charles R Greathouse IV_, Nov 30 2017

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Nov 30 2017